Method of scalable gray coding

ABSTRACT

A method for generating a modulo Gray-code representation of a non-power-of-two set of binary values begins by determining a desired Gray-code sequence length. The method then continues by determining a bus width, M, in bits, based on the desired Gray-code sequence length, to represent the generated Gray-code. The method then continues by determining a set of skipped binary values based on the desired Gray-code sequence length and the bus width to obtain the non-power-of-two set of binary values. The method then continues by representing the non-power-of-two set of binary values as a set of equivalent Gray-code values.

[0001] This patent application is claiming priority under 35 USC § 120to co-pending patent application entitled A SCALABLE GRAY CODE COUNTERAND APPLICATIONS THEREOF, having a filing date of Dec. 16, 2002 and aSer. No. 10/320,282.

TECHNICAL FIELD OF THE INVENTION

[0002] This invention relates generally to computing devices, and, moreparticularly to data communication systems comprising such devices. Evenmore particularly, the present invention relates to integrated circuitdesign using Gray Code within such communication systems.

BACKGROUND OF THE INVENTION

[0003] Communication systems are known to support wireless andwire-lined communications between wireless and/or wire-linedcommunication devices. Such communication systems range from nationaland/or international cellular telephone systems to the Internet topoint-to-point in-home wireless networks. Each type of communicationsystem is constructed, and hence operates, in accordance with one ormore communication standards. For instance, wireless communicationsystems may operate in accordance with one or more standards including,but not limited to, IEEE 802.11, Bluetooth, advanced mobile phoneservices (AMPS), digital AMPS, global system for mobile communications(GSM), code division multiple access (CDMA), local multi-pointdistribution systems (LMDS), multi-channel-multi-point distributionsystems (MMDS), and/or variations thereof.

[0004] Depending on the type of wireless communication system, awireless communication device, such as a cellular telephone, two-wayradio, personal digital assistant (PDA), personal computer (PC), laptopcomputer, home entertainment equipment, et cetera, communicates directlyor indirectly with other wireless communication devices. For directcommunications (also known as point-to-point communications), theparticipating wireless communication devices tune their receivers andtransmitters to the same channel or multiple channels (e.g., one or moreof the plurality of radio frequency (RF) carriers of the wirelesscommunication system) and communicate over that channel or channels. Forindirect wireless communications, each wireless communication devicecommunicates directly with an associated base station (e.g., forcellular services) and/or an associated access point (e.g., for anin-home or in-building wireless network) via an assigned channel, orchannels. To complete a communication connection between the wirelesscommunication devices, the associated base stations and/or associatedaccess points communicate with each other directly, via a systemcontroller, via the public switch telephone network, via the internet,and/or via some other wide area network.

[0005] For each wireless communication device to participate in wirelesscommunications, it includes a built-in radio transceiver (i.e., receiverand transmitter) or is coupled to an associated radio transceiver (e.g.,a station for in-home and/or in-building wireless communicationnetworks, RF modem, etc.). As is known, the receiver receives RFsignals, demodulates the RF carrier frequency from the RF signals toproduce baseband signals, and demodulates the baseband signals inaccordance with a particular wireless communication standard torecapture the transmitted data. The receiver is coupled to an antennaand includes a low noise amplifier, one or more intermediate frequencystages, a filtering stage, and a data recovery stage. The low noiseamplifier receives inbound RF signals via the antenna and amplifiesthem. The one or more intermediate frequency stages mix the amplified RFsignals with one or more local oscillations to convert the amplified RFsignals into the baseband signals or intermediate frequency (IF)signals. The filtering stage filters the baseband signals or the IFsignals to attenuate unwanted out-of-band signals to produce filteredsignals. The data recovery stage recovers raw data from the filteredsignals in accordance with the particular wireless communicationstandard.

[0006] As is also known, the transmitter converts data into RF signalsby modulating the data to produce baseband signals and mixing thebaseband signals with an RF carrier to produce RF signals. Thetransmitter includes a data modulation stage, one or more intermediatefrequency stages, and a power amplifier. The data modulation stageconverts the raw data into baseband signals in accordance with aparticular wireless communication standard. The one or more intermediatefrequency stages mix the baseband signals with one or more localoscillations to produce the RF signals. The power amplifier amplifiesthe RF signals prior to transmission via the antenna.

[0007] Further, data transmissions are serial streams of data, butwithin a network component (e.g., switch, relay, bridge, gateway, etcetera) the data is processed in parallel. It is a function of thetransceiver within each communication device or network component toconvert data from a serial to a parallel form, or vice-versa. Ingeneral, the transmitter converts parallel data into serial data andsources the serial data onto a communications link. A receiver receivesserial data via a communications link and converts it into paralleldata. A critical function of the receiver is to accurately sample thereceived serial data to be able to produce the parallel data.

[0008] As communication systems have become more advanced, and as theirdata capacity has increased, buffering of incoming and outgoing data hasbecome essential. Buffering of data allows a host device to attend toother tasks on a time-multiplexed basis during a communications session.For example, buffering is used to hold multiple communication sessionssimultaneously, to perform signal modulation and demodulation and toperform error correction. In addition, buffering can facilitateasynchronous communications, making it unnecessary for communicationdevices to share a common time base.

[0009] Buffering is commonly accomplished using RAM-based FIFOs. A FIFOis a first-in-first-out (FIFO) device in which data is temporarilystored in random-access memory (RAM). When a suitable unit, e.g., abyte, of data is received by the FIFO, the data unit is stored at a FIFOaddress indicated by a write pointer. Once that data is stored, thewrite pointer is incremented to the next FIFO address, which is wherethe next unit of received data will be stored. When a device is ready toread from the FIFO, it reads from a FIFO address indicated by a readpointer. After the data is read, the read pointer is incremented so thatthe next read is from the next FIFO address. Each pointer is basically acounter that counts data transfers. The counters are modulo in that theywrap to zero when a maximum count is reached.

[0010] Counters are used extensively in the design of integratedcircuits. For example, conventional binary-code counters can be used asFIFO pointers. Binary counter design is mature enough that, by enteringa few specifications (such as the counter range and speed), a computercan provide an optimized counter design. With a binary counter, however,there can be many bit differences in the representation of two adjacentbinary numbers. A disadvantage of binary counters, therefore, is thatthere can be considerable ambiguity when a count is read during a counttransition. For example, when a count increments from 011=3 to 100=4,every bit value changes. However, the changes can take place at slightlydifferent times across the bit positions. If the count is used in thesame clock domain, this is not a big problem. However, when the count isused in more than one clock domain (e.g., in an asynchronous circuitdesign), ambiguity can result as to the correct count.

[0011] For example, in a RAM-based asynchronous FIFO, the status of theFIFO (i.e., whether a data unit is present in the FIFO) is determined bycomparing the read pointer and the write pointer. However, because theread pointer and the write pointer are in different clock domains,direct comparison will not generate a reliable result. For example, whenthe count increments from 011=3 to 100=4, any of eight possible 3-bitbinary values might be read during the transition. This simultaneoustransition of a large number of bits can increase the risk of transitionerrors and can increase the electrical noise generated by the circuitry.Attempts to design around such extreme ambiguities can add considerablecomplexity to the counter or to circuit elements that respond to thecounter.

[0012] To avoid the problems with binary counters, “Gray Code” countersare often used. Gray code is an alternative to binary code that requiresa change in only one bit position between adjacent numbers. An example3-bit Gray-code sequence can be: 0=000, 1=001, 2=011, 3=010, 4=110,5=111, 6=101, and 7=100. Incrementing the last value, 100, yields thefirst value 000. Since only one bit position changes during a unitincrement, the only possible reads during a transition are the valuebeing changed from and the value being changed to. It is much easier todesign around this limited ambiguity than it is to design around themuch more extensive ambiguities associated with binary counter reads.Further, in an asynchronous circuit, a Gray-code counter's count can betransferred among the different clock domains without the noise andtransition errors of a binary counter.

[0013] While Gray-codes are well known in the art and can be readilyconstructed for any bit length, Gray-code counters are more complex anddifficult to design. Further, Gray-code counters are not readily scaled.Some prior art solutions addressing these problems exist. For example, atypical prior art Gray-code counter comprises a count register forstoring a Gray-code value, a Gray-to-binary code translator forconverting the stored Gray-code value to a corresponding binary-codevalue, a binary-code incrementer for incrementing the binary-code value,and a binary-Gray-code translator for converting the incrementedbinary-code value to the corresponding Gray-code value. However, anotherlimitation of Gray-code is that it requires an integer depth that is apower of two. Thus, a disadvantage of prior art Gray-code counters isthat, when the target FIFO depth is not a power of two, the FIFO designhas excess capacity. For example, when a communications application onlyrequires a FIFO depth of 78, the power-of-two limitation requires theuse of a 128-address FIFO.

[0014] In contrast, binary-code counters can be designed for anypositive integer depth. The discrepancy between target andGray-code-imposed capacities can be much greater for larger FIFOs,resulting in the inability to use a prior art Gray-code counter becauseof size and/or costs constraints in terms of integrated circuit area andbecause an oversized FIFO may be too slow for the particularapplication.

[0015] Some prior art solutions to these problems do exist. Thesesolutions comprise skipping certain binary values while maintaining theGray-code nature of the count. However, a very complex algorithm is usedin these prior art solutions to determine which binary values to skip.These solutions thus require a computer and associated software to runthe algorithm and determine the Gray-code pattern for a given modulonumber. For especially large modulo numbers (FIFO size), the Gray-codepattern will have to be stored on the integrated circuit for rapidaccess. Further, when determining the FIFO status, the counter data mustbe transformed from a Gray-code pattern, to a binary pattern, and backto a Gray-code pattern. Having to perform the complex algorithm twiceinvolves a heavy cost in time and efficiency.

[0016] Therefore, a need exists for a Gray-code counter and a binaryincrementer-decrementer algorithm therefore that can reduce or eliminatethe complexity and efficiency problems associated with the prior art.

BRIEF SUMMARY OF THE INVENTION

[0017] The method of scalable gray scale coding of the present inventionsubstantially meet these needs and others. In one embodiment, a methodfor generating a modulo Gray-code representation of a non-power-of-twoset of binary values begins by determining a desired Gray-code sequencelength. The method then continues by determining a bus width, M, inbits, based on the desired Gray-code sequence length, to represent thegenerated Gray-code. The method then continues by determining a set ofskipped binary values based on the desired Gray-code sequence length andthe bus width to obtain the non-power-of-two set of binary values. Themethod then continues by representing the non-power-of-two set of binaryvalues as a set of equivalent Gray-code values.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0018]FIG. 1 is a schematic block diagram of a wireless communicationsystem in accordance with the present invention;

[0019]FIG. 2 is a schematic block diagram of a wireless communicationdevice in accordance with the present invention;

[0020]FIG. 3 is a schematic block diagram of an optical interface inaccordance with the present invention;

[0021]FIG. 4 is a schematic block diagram of a Gray-codeincrementer-decrementer in accordance with the present invention;

[0022]FIG. 5 is a schematic block diagram of a modulo N Gray-codecounter in accordance with the present invention;

[0023]FIG. 6 is a flowchart of a method of operating a non-power-of-twomodulo N Gray-code counter in accordance with the present invention;

[0024]FIG. 7 a flowchart of a method for generating a modulo Gray-coderepresentation of a non-power-of-two set of binary values in accordancewith the present invention; and

[0025]FIG. 8 is a schematic block diagram of an apparatus implementingan embodiment of the non-power-of-two modulo N Gray-code counter inaccordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0026]FIG. 1 is a schematic block diagram illustrating a communicationsystem 10 that includes a plurality of base stations and/or accesspoints 12-16, a plurality of wireless communication devices 18-32 and anetwork hardware component 34. The wireless communication devices 18-32may be laptop host computers 18 and 26, personal digital assistant hosts20 and 30, personal computer hosts 24 and 32 and/or cellular telephonehosts 22 and 28. The details of the wireless communication devices willbe described in greater detail with reference to FIG. 2. Thenon-power-of-two modulo N Gray-code counter (the “Gray-code counter”)and binary incrementer-decrementer algorithm of the present inventioncan be incorporated within any of base stations and/or access points12-16, wireless communication devices 18-32 and network hardwarecomponent 34. For example, embodiments of the present invention can beimplemented as a pointer for a first-in-first-out (FIFO) within acommunications buffering scheme.

[0027] The base stations or access points 12-16 are operably coupled tothe network hardware 34 via local area network connections 36, 38 and40. The network hardware 34, which may be a router, switch, bridge,modem, system controller, et cetera provides a wide area networkconnection 42 for the communication system 10. Each of the base stationsor access points 12-16 has an associated antenna or antenna array tocommunicate with the wireless communication devices in its area.Typically, the wireless communication devices register with a particularbase station or access point 12-14 to receive services from thecommunication system 10. For direct connections (i.e., point-to-pointcommunications), wireless communication devices communicate directly viaan allocated channel. Typically, base stations are used for cellulartelephone systems and like-type systems, while access points are usedfor in-home or in-building wireless networks. Regardless of theparticular type of communication system, each wireless communicationdevice includes a built-in radio and/or is coupled to a radio.

[0028]FIG. 2 is a schematic block diagram illustrating a wirelesscommunication device that includes the host device 18-32 and anassociated radio 60. For cellular telephone hosts, the radio 60 is abuilt-in component. For personal digital assistants hosts, laptop hosts,and/or personal computer hosts, the radio 60 may be built-in or anexternally coupled component.

[0029] As illustrated, the host device 18-32 includes a processingmodule 50, memory 52, radio interface 54, input interface 58 and outputinterface 56. The processing module 50 and memory 52 execute thecorresponding instructions that are typically done by the host device.For example, for a cellular telephone host device, the processing module50 performs the corresponding communication functions in accordance witha particular cellular telephone standard.

[0030] The radio interface 54 allows data to be received from and sentto the radio 60. For data received from the radio 60 (e.g., inbounddata), the radio interface 54 provides the data to the processing module50 for further processing and/or routing to the output interface 56. Theoutput interface 56 provides connectivity to an output display devicesuch as a display, monitor, speakers, et cetera such that the receiveddata may be displayed. The radio interface 54 also provides data fromthe processing module 50 to the radio 60. The processing module 50 mayreceive the outbound data from an input device such as a keyboard,keypad, microphone, et cetera via the input interface 58 or generate thedata itself. For data received via the input interface 58, theprocessing module 50 may perform a corresponding host function on thedata and/or route it to the radio 60 via the radio interface 54.

[0031] Radio 60 includes a host interface 62, digital receiverprocessing module 64, an analog-to-digital converter 66, afiltering/attenuation module 68, an IF mixing down conversion stage 70,a receiver filter 71, a low noise amplifier 72, a transmitter/receiverswitch 73, a local oscillation module 74, memory 75, a digitaltransmitter processing module 76, a digital-to-analog converter 78, afiltering/gain module 80, an IF mixing up conversion stage 82, a poweramplifier 84, a transmitter filter module 85, and an antenna 86. Theantenna 86 may be a single antenna that is shared by the transmit andreceive paths as regulated by the transmit/receive switch 73, or mayinclude separate antennas for the transmit path and the receive path.The antenna implementation will depend on the particular standard towhich the wireless communication device is compliant.

[0032] The digital receiver processing module 64 and the digitaltransmitter processing module 76, in combination with operationalinstructions stored in memory 75, execute digital receiver functions anddigital transmitter functions, respectively. The digital receiverfunctions include, but are not limited to, digital intermediatefrequency to baseband conversion, demodulation, constellation demapping,decoding, and/or descrambling. The digital transmitter functionsinclude, but are not limited to, scrambling, encoding, constellationmapping, modulation, and/or digital baseband to IF conversion. Thedigital receiver and transmitter processing modules 64 and 76 may beimplemented using a shared processing device, individual processingdevices, or a plurality of processing devices. Such a processing devicemay be a microprocessor, micro-controller, digital signal processor,microcomputer, central processing unit, field programmable gate array,programmable logic device, state machine, logic circuitry, analogcircuitry, digital circuitry, and/or any device that manipulates signals(analog and/or digital) based on operational instructions. The memory 75may be a single memory device or a plurality of memory devices. Such amemory device may be a read-only memory, random access memory, volatilememory, non-volatile memory, static memory, dynamic memory, flashmemory, and/or any device that stores digital information. Note thatwhen the processing module 64 and/or 76 implements one or more of itsfunctions via a state machine, analog circuitry, digital circuitry,and/or logic circuitry, the memory storing the corresponding operationalinstructions is embedded with the circuitry comprising the statemachine, analog circuitry, digital circuitry, and/or logic circuitry.

[0033] In operation, the radio 60 receives outbound data 94 from thehost device via the host interface 62. The host interface 62 routes theoutbound data 94 to the digital transmitter processing module 76, whichprocesses the outbound data 94 in accordance with a particular wirelesscommunication standard (e.g., IEEE 802.11a, IEEE 802.11b, Bluetooth, etcetera) to produce digital transmission formatted data 96. The digitaltransmission formatted data 96 will be a digital base-band signal or adigital low IF signal, where the low IF typically will be in thefrequency range of one hundred kilohertz to a few megahertz.

[0034] The digital-to-analog converter 78 converts the digitaltransmission formatted data 96 from the digital domain to the analogdomain. The filtering/gain module 80 filters and/or adjusts the gain ofthe analog signal prior to providing it to the IF mixing stage 82. TheIF mixing stage 82 directly converts the analog baseband or low IFsignal into an RF signal based on an output oscillation provided bylocal oscillation module 74. The power amplifier 84 amplifies the RFsignal to produce outbound RF signal 98, which is filtered by thetransmitter filter module 85. The antenna 86 transmits the outbound RFsignal 98 to a targeted device such as a base station, an access pointand/or another wireless communication device.

[0035] The radio 60 also receives an inbound RF signal 88 via theantenna 86, which was transmitted by a base station, an access point, oranother wireless communication device. The antenna 86 provides theinbound RF signal 88 to the receiver filter module 71 via the Tx/Rxswitch 73, where the Rx filter 71 bandpass filters the inbound RF signal88. The Rx filter 71 provides the filtered RF signal to low noiseamplifier 72, which amplifies the signal 88 to produce an amplifiedinbound RF signal. The low noise amplifier 72 provides the amplifiedinbound RF signal to the IF mixing module 70, which directly convertsthe amplified inbound RF signal into an inbound low IF signal orbaseband signal based on a receiver local oscillation 81 provided bylocal oscillation module 74. The down conversion module 70 provides theinbound low IF signal or baseband signal to the filtering/gain module68. The filtering/gain module 68 filters and/or gains the inbound low IFsignal or the inbound baseband signal to produce a filtered inboundsignal.

[0036] The analog-to-digital converter 66 converts the filtered inboundsignal from the analog domain to the digital domain to produce digitalreception formatted data 90. The digital receiver processing module 64decodes, descrambles, demaps, and/or demodulates the digital receptionformatted data 90 to recapture inbound data 92 in accordance with theparticular wireless communication standard being implemented by radio60. The host interface 62 provides the recaptured inbound data 92 to thehost device 18-32 via the radio interface 54. Embodiments of theGray-code counter and binary incrementer-decrementer algorithm of thisinvention can be implemented within any of base stations and/or accesspoints 12-16, wireless communication devices 18-32, network hardwarecomponent 34, and/or radio 60 at any communications interface requiringbuffering of received and/or transmitted data, modulation ordemodulation, crossing of a clock boundary (for asynchronouscommunications), or memory storage.

[0037]FIG. 3 is a schematic block diagram of an optical interface 100within, for example, network hardware component 34, that includesnetwork interface processors 112 and 114, optical transmitters 116 and118, optical receivers 120 and 122 and optical links 124 and 126. Eachoptical link 124 and 126 may support one or more serial data streams ata rate specified by SONET or other fiber optic communication standard.Embodiments of the Gray-code counter and binary incrementer-decrementeralgorithm of this invention can be implemented within any of networkinterface processors 112 and 114, optical transmitters 116 and 118,and/or optical receivers 120 and 122 to replace traditional Gray-codecounters that may otherwise be used in buffering, memory storage orother counter applications.

[0038] In general, data is transceived via the network interfaceprocessors 112 and 114, which may be included in a network componentsuch as a switch, a bridge, a relay, a router, and/or any other type ofnetwork component used in fiber optic networks, the Internet, publicswitch telephone network, and/or any other wide area network or localarea network. As shown, the data provided by network interface processor112 to optical transmitter 116 is in a parallel format. The opticaltransmitter 116 converts the parallel data into serial data that istransmitted via optical link 124. Optical receiver 120 receives theserial data and converts it back into parallel data, which is providedto network interface processor 114.

[0039] Similarly, network interface processor 114 provides parallel datato optical transmitter 118. Optical transmitter 118 converts theparallel data into serial data and communicates it via optical link 126to optical receiver 122. Optical receiver 122 converts the serial datainto parallel data and provides the parallel data to network interfaceprocessor 112.

[0040] As one of average skill in the art will appreciate, the opticalinterface 100 corresponds generally to any interface within any type ofdigital communication system that employs serial data transmissionbetween devices. Accordingly, the optical links 124 and 126 may bereplaced by radio frequency links, microwave links, wires, et cetera.Accordingly, the concepts of the present invention are equallyapplicable in optical communication systems as well as any other type ofdigital communication system.

[0041]FIG. 4 is a schematic block diagram of a Gray-codeincrementer-decrementer 150 in accordance with the teachings of thisinvention. Gray-code incrementer-decrementer 150 comprisesGray-to-binary converter 152, binary incrementer-decrementer 154 andbinary-to-Gray converter 156. Gray-to-binary converter 152 receives asan input an M-bit Gray-code value 158, expressed as bit valuesI_(G)[0]-I_(G)[M−1], in order of increasing significance. M-bitGray-code value 158 can be, for example, the prior count input to aGray-code counter incorporating the Gray-code incrementer-decrementer150, as is discussed in greater detail with reference to FIG. 5.Gray-to-binary converter 152 converts the M-bit Gray-code value 158 to abinary equivalent M-bit binary input value 160, expressed as bit valuesI_(B[)0]-I_(B)[M−1]. The most-significant binary bit of M-bit binaryinput value 160 is the same as the most-significant Gray-code bit ofM-bit Gray-code value 158, and so on. Gray-to-binary converter 152 canbe any Gray-to-binary converter as known to those in the art.

[0042] Binary incrementer-decrementer (BIN) 154 receives the M-bitbinary input value 0.160 and converts it to an incremented ordecremented M-bit binary output value 162, expressed as bit valuesO_(B)[0]-O_(B)[M−1]. In most cases, M-bit binary output value 162 is oneunit greater or one unit less than M-Bit binary input value 160, as withconventional prior-art incrementers-decrementers. However, to providefor non-power-of-two modulo N Gray-code counters, BIN 154 of thisinvention includes a binary incrementer-decrementer algorithm (BINalgorithm) for skipping certain binary values while maintaining theGray-code nature of the output of Gray-code incrementer-decrementer 150.

[0043] BIN 154 skips certain binary values, which are determined basedon the integer depth (range), N, of the Gray-codeincrementer-decrementer 150, and the bus width in bits, M, used torepresent the Gray-code and binary values. The integer depth N is aneven whole number and can also represent the range of, for example, acounter incorporating Gray-code incrementer-decrementer 150, or theaddress range of a RAM-based FIFO buffer. Once the value of N isdetermined, for example, by the desired range of a Gray-code counter fora given application, the bus width, M, is obtained by determining avalue of 2^(M) that is greater than or equal to N, where M is a positivewhole value. The preferred value of M is typically obtained by using thesmallest value of 2^(M) that is greater than or equal to N. For example,for a modulo 6 Gray-code counter (i e., a Gray-code counter having arange of N=6), the value of M can be 3 (i.e., 23 is the smallest powerof two greater than or equal to six).

[0044] For a given value of N and M, the embodiments of the BINalgorithm of this invention can then determine the binary values for BIN154 to skip according to one of the algorithms disclosed below. Itshould be noted that in any embodiment of the BIN algorithm of thisinvention, the number of binary values skipped is equal to S, whereS=2^(M)-N. This should be easy to see, since if the range of BIN 154 isN, a standard power-of-two Gray-code input to Gray-to-binary converter152 will have a range of 2^(M) Gray-code values. To obtain thenon-power-of-two modulo N Gray-code incrementer-decrementer 150functionality in accordance with the teachings of this invention, therange of values in excess of N must be eliminated. Thus, if BIN 154 isimplemented as an incrementer, then in one embodiment BIN 154 incrementsM-bit binary input value 160 according to the BIN logic algorithm:

[0045] IF I_(B)[m−1:0]=2^(M−1)+N/2−1, THEN

[0046] O_(B)[m−1:0]=2^(M−1)−N/2

[0047] ELSE

[0048] O_(B)[m−1:0]=I_(B)[m−1:0]+1

[0049] In a similar manner, BIN 154 decrements M-bit binary input value160 according to the corresponding decrementing BIN logic algorithm:

[0050] IF I_(B)[m−1:0]=2^(M−1)−N/2, THEN

[0051] O_(B)[m−1:0]=2^(M−1)+N/2−1

[0052] ELSE

[0053] O_(B)[m−1:0]=I_(B)[m−1:0]−1.

[0054] The incrementer-decrementer logic algorithms disclosed above havethe effect of skipping the first S/2 binary values and the last S/2binary values of a sequential set of 2^(M) M-bit binary input values160. The remaining set of binary values comprises a non-power-of-two setof binary values, which when converted from binary-code to Gray-code bybinary-to-Gray converter 156, will preserve the Gray-code nature of theBIN 154. For example, a BIN 154 with a range of modulo 12 (N=12) has abus width M=4 (i.e., with 2^(M)=16, M=4). S is then equal to 16−12=4.Thus, a total of 4 binary values will be skipped, one half (2) at thebeginning of the sequential set of 2^(M) M-bit binary input values 160,and the remaining half at the end of the sequential set of 2^(M) M-bitbinary input values 160.

[0055] In another embodiment of the BIN algorithm of this invention, ifBIN 154 is implemented as an incrementer, then BIN 154 increments M-bitbinary input value 160 according to the BIN logic algorithm:

[0056] IF I_(B)[m−1:0]=N/2−1, THEN

[0057] O_(B)[m−1:0]=2^(M)−N/2

[0058] ELSE

[0059] O_(B)[m−1:0]=I_(B)[m−1:0]+1

[0060] In a similar manner, BIN 154 decrements M-bit binary input value160 according to the corresponding decrementing BIN logic algorithm:

[0061] IF I_(B)[m−1:0]=2^(M)−N/2, THEN

[0062] O_(B)[m−1:0]=N/2−1

[0063] ELSE

[0064] O_(B)[m−1:0]=I_(B)[m−1:0]−1.

[0065] The incrementer-decrementer logic algorithms of the secondembodiment disclosed above have the effect of skipping the middle Sbinary values of a sequential set of 2^(M) M-bit binary input values160. The remaining set of binary values again comprises anon-power-of-two set of binary values, which when converted frombinary-code to Gray-code by binary-to-Gray converter 156, will preservethe Gray-code nature of the BIN 154. For the same modulo 12 examplediscussed above with reference to the first embodiment of the BINalgorithm, the second embodiment of the BIN algorithm will result inskipping of the middle 4 binary values of the sequential set of 2^(M)M-bit binary input values 160.

[0066] The embodiments of the BIN 154 of this invention, and of aGray-code counter incorporating BIN 154, thus provide a Gray-codecounter for any even modulo number. For a power-of-two modulo number,the Gray-code counter of this invention reduces to a conventionalGray-code counter. For a non-power-of-two modulo number, however, theembodiments of this invention will skip binary values as disclosed aboveto generate a Gray-code representation of a non-power-of-two set ofbinary values. The modulo 12 example discussed above is summarized inthe following Table 1 for both disclosed embodiments. In this example,the sequential set of 2^(M) M-bit binary input values 160 comprises thebinary values 0-15. TABLE 1 [ ] Skipped by first embodiment; { } Skippedby second embodiment. DECIMAL VALUE BINARY VALUE GRAY-CODE VALUE  [0][0000] [0000]  [1] [0001] [0001]  2 0010 0011  3 0011 0010  4 0100 0110 5 0101 0111  {6} {0110} {0101}  {7} {0111} {0100}  {8} {1000} {1100} {9} {1001} {1101} 10 1010 1111 11 1011 1110 12 1100 1010 13 1101 1011[14] [1110] [1001] [15] [1111] [1000]

[0067] As indicated by inspection of Table 1, if no values are skipped,Table 1 corresponds to a 4-bit Gray-code incrementer-decrementer (orassociated Gray-code counter) with sixteen distinct values. The middlecolumn corresponds to the BIN 154. To achieve a Gray-codeincrementer-decrementer 150 with twelve distinct values, the presentinvention provides for skipping 4 values, e.g., decimal values 0, 1, 14,and 15 for a first embodiment, or decimal values 6-9 for a secondembodiment of the BIN algorithm, as indicated by the respectiveparentheses in Table 1. Thus, in the first embodiment, when the decimalcount is 13, the Gray-code count is 1011, which is translated asbinary-code 1101. When this is incremented by BIN 154, the result is2=0010 binary-code. This will be converted to 2=0011 Gray-code. 2=0011Gray-code differs from 13=1011 at only the first position. The Gray-codenature of the count sequence is thus preserved.

[0068] Conventional Gray-code (as shown in the last column of Table 1)is well known. Gray-codes cab be readily constructed for any bit length.A one-bit Gray-code can be the same as a one-bit binary-code. Thesequence is 0,1. A two-bit Gray-code can be generated form a one-bitGray-code using the following algorithm. First, the sequence is copiedto yield 0,1;01. Then, the second copy is reversed to yield 0,1;1,0.Lastly, leading zeroes are added to the values in the first copy andleading ones are added to the values in the second copy to yield00,01,11,10. This is a two-bit Gray-code. The same algorithm can beapplied to the two-bit Gray-code to yield a three-bit Gray-code, and canbe further iterated to yield Gray-codes of any bit length. Such aconventional Gray-code is the basis for conversion by BIN 154 into anon-power-of-two Gray-code in accordance with the teachings of thisinvention.

[0069] Binary-to-Gray converter 156 of FIG. 4 converts the M-bit binaryoutput value 162 to a Gray-code equivalent M-bit Gray-code output value164, expressed as bit values O_(G)[0]-O_(G)[M−1]. The most-significantGray-code bit of M-bit Gray-code output value 164 is the same as themost-significant binary bit of M-bit binary output value 162, and so on.Binary-to-Gray converter 156 can be any binary-to-Gray converter asknown to those in the art.

[0070]FIG. 5 is a schematic block diagram of a modulo N Gray-Codecounter 200 incorporating Gray-code incrementer-decrementer 150 of FIG.4. Gray-code counter 200 includes Gray-code incrementer-decrementer 150,the operation of which is disclosed with regards to FIG. 4, and an M-bitclocked storage device 210. M-bit clocked storage device 210 can be anM-bit register. M-bit clocked storage device 210 comprises M D-typeflip-flops 230 clocked by clock 220. M-bit clocked storage device 210stores an M-bit Gray-code count, expressed as bit valuesQ_(G)[0]-Q_(G)[M−1]. This count is the output of Gray-code counter 200and is also the input to Gray-code incrementer-decrementer 150 (i.e.,the input to Gray-to-Binary converter 152), expressed as M-bit Gray-codevalue 158 bit values I_(G)[0]-I_(G)[M−1].

[0071] Upon receipt of a clock signal at its clock inputs, M-bit clockedstorage device 210 replaces the stored M-bit Gray-code countQ_(G)[0]-Q_(G)[M−1] with the next M-bit Gray-code count (M-bit Gray-codeoutput value 164). The Gray-code incrementer-decrementer 150 of thepresent invention, together with M-bit clocked storage device 210, canprovide a non-power-of-two modulo N Gray-code counter 200, for any eveninteger depth value, that will preserve the Gray-code nature of thecounter. The output from Gray-code counter 200 can be, for example, thepointer value for a RAM-based FIFO.

[0072] The operation of Gray-code counter 200 of FIG. 5 is otherwise asdescribed for Gray-code incrementer-decrementer 150. M-bit clockedstorage device 210 provides the added functionality needed to turnGray-code incrementer-decrementer 150 into a Gray-code counter 200 inaccordance with the teachings of this invention. Gray-code counter 200implements a method of operating a non-power-of-two modulo N Gray-codecounter. This method is flow-charted in FIG. 6.

[0073] At step 300 of FIG. 6, a prior M-bit Gray-code input valueI_(G)[M−1:0] is converted to an M-bit binary-code input value 160,represented by the bit values I_(B)[M−1:0] (Note that for the purposesof this discussion, a range of bit values expressed as, for example,I_(B)[M−1:0], represents the same range of bit values asI_(B)[0]-I_(B)[M−1]). At step 302, the M-bit binary-code input value 160is converted to an M-bit binary-code output value 162, represented bybit values O_(B)[M−1:0], wherein the M-bit binary-code output value 162will differ from the M-bit binary-code input value 160 by modulo +/−1(one unit) for all but one value of the M-bit binary-code input value160. Step 302 occurs within BIN 154 and is implemented according to theembodiments of the BIN algorithm disclosed above.

[0074] At step 304, the M-bit binary-code output value is converted toan M-bit Gray-code output value 164 (O_(G)[M−1:0]). The M-bit Gray-codeoutput value 164 is stored at step 306 based upon receipt of a clocksignal and, at step 308, upon receipt of a next clock signal, the M-bitGray-code output value 164 is provided as a next M-bit Gray-code inputvalue 158 (I_(G)[M−1:0]) to supercede the prior M-bit Gray-code inputvalue 158 of step 300. The method then repeats on subsequent clocksignals to provide the counter functionality of a Gray-code counter 200designed and operated in accordance with the teachings of thisinvention.

[0075] The present invention provides a convenient method for generatinga modulo Gray-code representation of a non-power-of-two set of binaryvalues. This method corresponds to the embodiments of the BIN algorithmdisclosed above in that it can be used to determine the number andsequential location of the binary values to be skipped. The method isflow-charted in FIG. 7.

[0076] At step 350, a desired Gray-code sequence length is determined.The Gray-code sequence length is equal to the value N, and cancorrespond to the desired range of a modulo Gray-code counter 200, or tothe depth of a FIFO buffer associated with a Gray-code counter 200. N isan even whole number and can be a non-power-of-two value. At step 360, abus width, M, in bits is determined based on the desired Gray-codesequence length to represent the generated Gray-code. The value of M isobtained by determining a value of 2^(M) that is greater than or equalto N, where M is a positive whole value. The preferred value of M istypically obtained by using the smallest value of 2^(M) that is greaterthan or equal to N. At step 370, a set of skipped binary values isdetermined based on the Gray-code sequence length and the bus width toobtain the non-power-of-two set of binary values. At step 380, thenon-power-of-two set of binary values is represented as a set ofequivalent Gray-code values obtained in a traditional conversion frombinary to Gray-code.

[0077] Step 370 can be accomplished in a number of ways. In oneembodiment, corresponding to the first embodiment of the BIN algorithmof this invention disclosed above, step 370 comprises determining aninitial set of 2^(M) sequential binary values; determining a number, S,of binary values to skip, where S=2^(M)-N; eliminating from the initialset of 2^(M) binary values the first S/2 binary values and the last S/2binary values; and populating the non-power-of-two set of binary valueswith the remaining sequential binary values. These binary values canthen be converted to an equivalent set of Gray-code values.

[0078] In another embodiment, corresponding to the second embodiment ofthe BIN algorithm of this invention disclosed above, step 370 comprisesdetermining an initial set of 2^(M) sequential binary values;determining a number, S, of binary values to skip, where S=2^(M)-N;eliminating from the initial set of 2^(M) sequential binary values themiddle S binary values; and populating the non-power-of-two set ofbinary values with the remaining sequential binary values. These binaryvalues can then be converted to an equivalent set of Gray-code values.

[0079] A further embodiment of the present invention can comprise anapparatus for non-power-of-two modulo N Gray-code counting. As shown inFIG. 8, the apparatus 400 can comprise a processing module 402 and amemory 404. Processing module 402 may be a single processing device or aplurality of processing devices. Such a processing device may be amicroprocessor, micro-controller, digital signal processor,microcomputer, central processing unit, field programmable gate array,programmable logic device, state machine, logic circuitry, analogcircuitry, digital circuitry, and/or any device that manipulates signals(analog and/or digital) based on operational instructions. The memory404 may be a single memory device or a plurality of memory devices. Sucha memory device may be a read-only memory, random access memory,volatile memory, non-volatile memory, static memory, dynamic memory,flash memory, and/or any device that stores digital information. Notethat when the processing module 402 implements one or more of itsfunctions via a state machine, analog circuitry, digital circuitry,and/or logic circuitry, the memory storing the corresponding operationalinstructions is embedded with the circuitry comprising the statemachine, analog circuitry, digital circuitry, and/or logic circuitry.The memory 404 stores, and the processing module 402 executes,operational instructions corresponding to at least some of the stepsand/or functions illustrated in FIGS. 4-7.

[0080] In a particular embodiment of apparatus 400, the memory 404 isoperably coupled to processing module 402 and includes operationalinstructions that cause the processing module 402 to convert an M-bitGray-code input value to an M-bit binary-code input value, I_(B)[m-1:0];convert the M-bit binary-code input value to an M-bit binary-code outputvalue, O_(B)[m-1:0], wherein the M-bit binary-code output value willdiffer from the M-bit binary-code input value by modulo +/−1 for all butone value of the M-bit binary-code input value; convert the M-bitbinary-code output value to an M-bit Gray-code output value; store theM-bit Gray-code output value based on a clock signal; and provide theM-bit Gray-code output value to the Gray-to-binary converter as a nextM-bit Gray-code input value upon a next clock signal. The step ofconverting the M-bit binary-code input value to an M-bit binary-codeoutput value, O_(B)[m-1:0] can be accomplished in accordance with theembodiments of the BIN algorithm of this invention as disclosed above.

[0081] The present invention provides for Gray-code counters and binaryincrementer-decrementer algorithms that have modulos that are not powersof two. Optimal FIFO sizes, for example, can therefore be accommodated.Further, the present invention can provide for more effective use ofintegrated circuit area. The present invention also provides a simplealgorithm for designing a non-power-of-two modulo N Gray-code counter. Acomputer program running, for example, synthesizable HDL (HardwareDescription Language) can easily generate Gray-code counter designs inaccordance with this invention for any given modulo.

[0082] As one of average skill in the art will appreciate, otherembodiments may be derived from the teaching of the present invention,without deviating from the scope of the claims.

What is claimed is:
 1. A method for generating a modulo Gray-coderepresentation of a non-power-of-two set of binary values, comprising:determining a desired Gray-code sequence length; determining a buswidth, M, in bits, based on the desired Gray-code sequence length, torepresent the generated Gray-code; determining a set of skipped binaryvalues based on the desired Gray-code sequence length and the bus widthto obtain the non-power-of-two set of binary values; and representingthe non-power-of-two set of binary values as a set of equivalentGray-code values.
 2. The method of claim 1, wherein the non-power-of-twoset of binary values comprises N values, where N is an even wholenumber, and wherein the Gray-code sequence length is equal to N.
 3. Themethod of claim 2, wherein determining the desired Gray-code sequencelength comprises determining the desired depth of a FIFO(first-in-first-out) buffer, and setting N equal to the depth of theFIFO buffer.
 4. The method of claim 2, wherein determining the bus widthM comprises determining the smallest value of 2^(M) that is greater thanor equal to N, where M is a positive whole value.
 5. The method of claim4, wherein determining the set of skipped binary values comprises:determining an initial set of 2^(M) sequential binary values;determining a number, S, of binary values to skip, where S=2^(M)-N;eliminating from the initial set of 2^(M) sequential binary values thefirst S/2 binary values and the last S/2 binary values; and populatingthe non-power-of-two set of binary values with the remaining sequentialbinary values.
 6. The method of claim 4, wherein determining the set ofskipped binary values comprises: determining an initial set of 2^(M)sequential binary values; determining a number, S, of binary values toskip, where S=2^(M)−N; eliminating from the initial set of ₂M sequentialbinary values the middle S binary values; and populating thenon-power-of-two set of binary values with the remaining sequentialbinary values.
 7. The method of claim 1, further comprising: determiningan initial set of 2^(M) sequential binary values, wherein thenon-power-of-two set of binary values is a subset of the initial set of2^(M) sequential binary values; and generating a Gray-coderepresentation of the initial set of 2^(M) sequential binary values. 8.The method of claim 7, wherein the initial set of 2^(M) sequentialbinary values comprises the values zero through 2^(M−1).